Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model

Abstract

It is possible to simulate the dynamics of a single spin-$1/2$ ($\mathsf{PT}$ symmetric) system by conveniently embedding it into a subspace of a larger Hilbert space with unitary dynamics. Our goal is to formulate a many body generalization of this idea i.e., embedding many body non-Hermitian dynamics. As a first step in this direction, we investigate embedding of "$N$" non-interacting spin-$1/2$ ($\mathsf{PT}$ symmetric) degrees of freedom, thereby unfolding the complex nature of such an embedding procedure. It turns out that the resulting Hermitian Hamiltonian represents a cluster of $N+1$ spin halves with "all to all", $q$-body interaction terms ($q=1,...,N+1$) in which the additional spin-$1/2$ is a part of the larger embedding space. We can visualize it as a strongly correlated central spin model with the additional spin-$1/2$ playing the role of central spin. We find that due to the orthogonality catastrophe, even a vanishing small exchange field applied along the anisotropy axis of the central spin leads to a strong suppression of its decoherence arising from spin-flipping perturbations.

arXiv comment10 pages, 5 figures

References in corpus (25)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Complex Extension of Quantum Mechanics
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• Introduction to PT-Symmetric Quantum Theory
• Observation of parity-time symmetry breaking in a single spin system
• Faster than Hermitian Quantum Mechanics
• Non-Hermitian Many-Body Localization
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• Observation of critical phenomena in parity-time-symmetric quantum dynamics
• Light stops at exceptional points
• Anomalous helical edge states in a non-Hermitian Chern insulator
• The Naimark dilated PT-symmetric brachistochrone
• Parity-time-symmetric topological superconductor
• Observation of PT-symmetric quantum interference
• Perfect State Transfer in PT-symmetric Non-Hermitian Networks
• Synthesizing three-body interaction of spin chirality with superconducting qubits
• Integrability and dark states in an anisotropic central spin model
• Simulating broken $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems by weak measurement
• PT-symmetric quantum state discrimination
• Arbitrary Nuclear Spin Gates in Diamond Mediated by a NV-center Electron Spin
• Persistent dark states in anisotropic central spin models
• Embedding, simulation and consistency of $\mathcal{P}\mathcal{T}$ -symmetric quantum Theory

Cited by in corpus (6)

• Quantum Algorithms for Open Lattice Field Theory
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• Practical quantum simulation of small-scale non-Hermitian dynamics
• Operator correlations in a quenched non-Hermitian Luttinger liquid
• Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme